Joty—On the Origin of the Canals of Mars. 267 
cases very many curves circling the planet are struck, as in the manner of the 
composition of simple harmonic motions—to which these curves are analogous— 
before the figure repeats itself. 
The several loops may or may not intersect upon the equator or off the equator 
according to the nature of the ratio of velocities determining the curve. 
If planet and satellite rotate at like angular velocities the retrograde curve 
will intersect upon the equator at one point, the span being 360°. If the 
curve is direct, it crosses the equator at one point with a span of 0°. In 
certain cases, as for example such a ratio as 1:8, the number of crossing points 
in each hemisphere is very considerable in each complete description of the 
curve, 
In the consideration as to the agreement of the curves with the theory that 
these originated in the near approach of satellites, I have confined myself to the 
map of Mr. Lowell. That Schiaparelli’s maps agree with Lowell’s, in so far as 
these overlap, is obvious on inspection. But the lines on Schiaparelli’s map are 
less definite, and differences exist between his earlier and later maps. I there- 
fore considered the more definite map of Lowell most suitable to this investiga- 
tion, as serving to apply, in fact, a more rigorous test to the hypothesis. Both 
observers ascribe the same general character to the curves, in that they are shown 
to be concave and generally symmetrical to the equator. 
The Radiants. 
No hypothesis as to the origin of the lines on Mars will be complete without 
extending to the disposition of these lines as in some cases radiating from certain 
centres. The crossing of the several loops of the curves will hardly account, 
without some auxiliary supposition, for the appearance presented by such a 
radiant as the Sinus Titanum, for example. 
It appears to me that the explanation of these radiants is indeed not to be 
looked for in this direction, but to be found in the effects of perturbations upon 
small satellites by raised surface features on Mars. ‘This is only offered here as a 
suggestion, for without more complete investigation and possibly without more 
knowledge than we at present possess, the effects and possibility of such pertur- 
bations must be pure guesswork. But in support of this suggestion it is to be 
observed that the radiants of pronounced character are situated upon the coast 
lines or at the larger oases or spots. The latter, according to the views in this 
Paper, are raised features, and raised features on the coast lines are in keeping 
with terrestrial physiography. Indeed dark triangular marks characterise these 
coast-line radiants. 
I assume that raised features may effect the path of a satellite both in swaying 
